Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample97.0ms

Algorithm

intervals

Results

44.0ms	94×	body	1280	valid
17.0ms	62×	body	640	valid
17.0ms	18×	body	2560	valid
7.0ms	36×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	11×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.6b	(sin.f64 (+.f64 x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series15.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	(sin.f64 (+.f64 x eps))

simplify53.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5348	268

prune25.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.4b

Counts

30 → 3

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

3 → 41

Calls

3 calls:

6.0ms	(+.f64 x (+.f64 x eps))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series22.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+.f64 x (+.f64 x eps))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5169	541

prune52.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Merged error: 0.3b

Counts

53 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`log-prod_binary64` `exp-prod_binary64`
8×	`pow1_binary64` `log-pow_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
3×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 61

Calls

4 calls:

11.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
15.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
8.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series33.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5064	940

prune58.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	73	8	81

Merged error: 0.3b

Counts

81 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.4b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
4.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series53.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
15.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
16.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify37.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5187	440

prune54.0ms

Filtered

45 candidates to 52 candidates (-15.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	52	8	60

Merged error: 0.3b

Counts

60 → 8

regimes105.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.1b

bsearch73.0ms

Steps

Iters	Range		Point
9	9.548151851389376e-12	4.798688009906535e-06	8.744386299618572e-09
8	-0.0045913724923496105	-1.0278274854661441e-05	-1.0409825245922592e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	3251×	body	1280	valid
574.0ms	572×	body	2560	valid
523.0ms	1850×	body	640	valid
159.0ms	815×	body	320	valid
77.0ms	1115×	body	80	valid
50.0ms	397×	body	160	valid

Details

analyze2.0ms

sample97.0ms

simplify7.0ms

prune9.0ms

localize9.0ms

rewrite13.0ms

series15.0ms

simplify53.0ms

prune25.0ms

localize15.0ms

rewrite23.0ms

series22.0ms

simplify67.0ms

prune52.0ms

localize16.0ms

rewrite45.0ms

series33.0ms

simplify53.0ms

prune58.0ms

localize16.0ms

rewrite17.0ms

series53.0ms

simplify37.0ms

prune54.0ms

regimes105.0ms

bsearch73.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling